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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">P</font> = <font color="Maroon" title="c2">P</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">k</font> <a href="qc_lang1.html#K7" title="QC_LANG1:func.7">-ary_QC-pred_symbols</a>  ;<br/>
<a NAME="E2:29"/>
<font color="Maroon" title="c3">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> :  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> </span>}</span> 
 
;<br/>
<a NAME="E3:29"/><b>then </b>
 ex <font color="Olive" title="b1">Q</font> being  <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> st <br/>( <font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Q</font> &amp;  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> )
 
;<br/>
<b>hence </b><a NAME="E4:29"/>
 <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font>
 ;<br/>


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